1. Field of the Invention
The present invention relates to inductors and in particular to the use of a switchable inductor to change the tuned frequency of a differential circuit.
2. Discussion of the Related Art
Radio-frequency (RF) integrated circuits commonly use a tuned circuit in which an on-chip inductor resonates with parasitic and non-parasitic capacitances. To tune the frequency of a tank, i.e. a parallel L/C (inductor/capacitor) circuit that can provide high impedance at the frequency of operation, variable capacitors can be used. For example, FIG. 1A illustrates a simplified, tunable gain stage 100 with variable capacitive tuning.
In FIG. 1A, a tank 101A is connected between a high voltage source VDD and a drain of an NMOS transistor 102A. The source of NMOS transistor 102A is connected to a drain of an NMOS transistor 103A. The source of NMOS transistor 103A is connected to a current source 104, which in turn is connected to a low voltage source VSS. Similarly, a tank 101B is connected between a high voltage source VDD and a drain of an NMOS transistor 102B. The source of NMOS transistor 102B is connected to a drain of an NMOS transistor 103B. The source of NMOS transistor 103B is connected to current source 104. In this configuration, tunable gain stage 100 can be implemented as a cascode amplifier, wherein voltage Vc can be a bias voltage of the gates of this amplifier. Voltages Vin(+) and Vin(−) represent the positive and negative voltages applied to gain stage 100.
Notably, a variable capacitor 105, which is connected between tanks 101A and 101B, allows gain stage 100 to be tuned capacitively. Variable capacitors can be implemented as fixed capacitors that are connected using switches. For example, FIG. 1B illustrates an exemplary implementation for variable capacitor 105 in gain stage 100. Specifically, variable capacitor 105 can be implemented as switchable capacitors 105A and 105B, wherein each switchable capacitor includes a capacitor and a switch (e.g. implemented using a transistor). FIG. 1C illustrates another exemplary implementation for variable capacitor 105 in which switchable capacitors 105A and 105B share a common switch.
Unfortunately, variable capacitors can have significant disadvantages. For example, variable capacitors can have significant capacitance even in the low capacitance state. Therefore, the inductor in the circuit must be smaller and the gain of the stage must be lower than if variable capacitance was not used.
Additionally, the performance in the low frequency band suffers because the equivalent parallel resistance is lower than in the higher frequency band. To better understand this phenomena, note that each tank has an associated loss. For example, FIG. 1D illustrates a tank 110 in which this associated loss can be shown as a parallel resistance Rp. Equation (1) computes the parallel resistance Rp for a tank in term of the series resistance Rs of the inductor and the quality factor Q.Rp=Rs(1+Q2)  Equation (1)Equation (2) recognizes that the quality factor Q is equivalent to Lw/Rs, wherein L is the inductance and w is the angular frequency of operation.Rp=Rs(1+(Lw/Rs)2)  Equation (2)Logically, referring to Equation (2), the parallel resistance Rp drops at lower frequencies.
However, note that w=1/√{square root over (LC)}, (Lw/Rs)2=L/CRs, wherein C is the capacitance. Thus, for higher performance (and thus higher parallel resistance Rp), the inductance L is preferably increased or the capacitance C decreased. Therefore, a need arises for a tunable differential circuit that can advantageously increase inductance.